3 (1/2" thick) slices good quality white sandwich bread, crusts discarded
1/2 cup whole milk
3/4 stick unsalted butter, divided
2 game hens, livers coarsely chopped and reserved for stuffing
1/2 teaspoon chopped thyme, divided
1/4 cup water
Preheat your oven to 375 and place rack in middle.
Arrange bread in 1 layer in a shallow dish and pour milk over it.
Soak bread, turning once, just until it has absorbed most of milk, about 2 minutes.
Squeeze excess milk from each slice, then tear bread into bite-size pieces, dropping them into a bowl, then discard milk.
Melt butter and add to bread along with livers, 1/4 teaspoon thyme, 1/4 teaspoon salt, and 1/8 teaspoon pepper, stirring to combine.
Rinse hens and pat dry, then chop off wing tips and scatter with nicks in a large shallow baking pan.
Divide stuffing among cavities of hens, then close openings with wooden toothpicks.
Tie legs of each hen together with string and secure wings to sides with wooden toothpicks.
Stir together 1/4 teaspoon salt, 1/8 teaspoon pepper, and remaining 1/4 teaspoon thyme and rub all over hens.
Arrange hens in baking pan (with necks and wing tips), without crowding, then cut remaining stick butter into 8 pieces and put 2 pieces on top of each bird.
Roast, basting with butter from pan every 8 to 10 minutes, until an thermometer inserted into a thigh reads 160, about 1 hour.
Transfer hens to a platter and let stand, loosely covered with foil, while making sauce.
Discard necks and wing tips and pour pan juices into fat separator.
Let stand 1 minute to allow fat to separate from juices.
Add water (1/4 cup) to pan and deglaze by boiling, stirring and scraping up brown bits, 1 to 2 minutes.
Transfer to a small saucepan along with pan juices and 1/8 cup fat from separator and simmer, whisking, until emulsified, about 1 minute.
Cut hens in half and serve with sauce on the side. Enjoy!